Universal Hyperbolic Geometry
Universal Hyperbolic Geometry (UNSW). This is a collection of video lectures on Universal Hyperbolic Geometry given by Professor N. J. Wildberger. This course explains a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity.
|Lecture 26 - Trigonometric Laws in Hyperbolic Geometry using Geometer's Sketchpad|
We use Geometer's Sketchpad to illustrate the four main laws of trigonometry in Universal Hyperbolic Geometry. These are Pythagoras' theorem, the Triple quad formula, the Spread law and the Cross law. We use custom tools to calculate quadrance and spread. We illustrate each law with a variety of examples. Along the way we show dual triangles, and explain some other features of GSP.
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